Relaxation strategy for the Landweber method

被引：21

作者：

Han, Guanghui ^{[1
]}

Qu, Gangrong ^{[1
,2
]}

Jiang, Ming ^{[3
,4
]}

机构：

[1] Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China

[2] Beijing Ctr Math & Informat Interdisciplinary Sci, Beijing 100048, Peoples R China

[3] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

[4] Peking Univ, Cooperat Medianet Innovat Ctr, Beijing 100871, Peoples R China

来源：

SIGNAL PROCESSING | 2016年 / 125卷

基金：

美国国家科学基金会;

关键词：

Landweber iteration; Relaxation strategy; Image reconstruction; Weighted least-squares; ITERATIVE ALGORITHMS; CONVERGENCE; SYSTEMS; ACCELERATION; PROJECTIONS;

D O I：

10.1016/j.sigpro.2016.01.010

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The Landweber iteration is a general method for the solution of linear systems which is widely applied for image reconstructions. The convergence behavior of the Landweber iteration is of both theoretical and practical importance. By the representation of the iterative formula and the convergence results of the Landweber iteration, we derive the optimal relaxation method under the minimization of the spectral radius of the newly derived iterative matrix. We also establish the iterative relaxation strategy to accelerate the convergence for the Landweber iteration when only the biggest singular value is available. As an immediate result, we derive the corresponding results for Richardson's iteration for the symmetric nonnegative definite linear systems. Finally, numerical simulations are conducted to validate the theoretical results. The advantage of the proposed relaxation strategies is demonstrated by comparing with the existing strategies. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：87 / 96

页数：10

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